Details

sample64.0ms

Algorithm

intervals

Results

32.0ms	92×	body	1280	valid
8.0ms	133×	body	80	valid
5.0ms	20×	body	640	valid
2.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify60.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	26	12
3	32	12
4	34	12
5	40	12
6	42	12
done	42	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize12.0ms

Local error

Found 1 expressions with local error:

1.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`prod-diff`
11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt`
3×	`fma-neg` `sqrt-prod` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 31

Calls

1 calls:

22.0ms

(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series522.0ms

Counts

1 → 3

Calls

1 calls:

522.0ms

(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.0s

Counts

34 → 34

Iterations

Useful iterations: 3 (915.0ms)

Iter	Nodes	Cost
0	122	1329
1	298	968
2	899	773
3	4118	657
done	5000	657

prune96.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.5b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

0.0b

(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

1.0b

(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`associate-/r*`
3×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u` `associate-/l*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

27.0ms

(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

6.0ms

(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

9.0ms

(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series2.2s

Counts

3 → 9

Calls

3 calls:

1.5s

(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

468.0ms

(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

158.0ms

(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.9s

Counts

80 → 80

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	272	3051
1	854	2885
2	3581	2645
done	5000	2637

prune451.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ (- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)
1.0b	(- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
99×	`unpow-prod-down`
80×	`*-un-lft-identity`
58×	`add-cube-cbrt`
56×	`prod-diff`
47×	`sqr-pow`
45×	`difference-of-squares`
42×	`times-frac`
14×	`associate-/l*`
10×	`distribute-lft-out--`
8×	`pow1` `sqrt-prod` `add-log-exp`
7×	`add-exp-log` `fma-neg`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/r*`
2×	`flip3--` `sqrt-pow1` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `sqrt-pow2` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 205

Calls

4 calls:

10.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
99.0ms	(/ (- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
24.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)
40.0ms	(- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))

series3.2s

Counts

4 → 12

Calls

4 calls:

433.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.5s	(/ (- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
708.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)
555.0ms	(- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))

simplify3.1s

Counts

217 → 217

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	518	11330
1	1346	9278
2	4547	7580
done	5000	7577

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)
1.0b	(log (exp (- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))))
1.0b	(- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

127×	`unpow-prod-down`
112×	`prod-diff`
95×	`add-sqr-sqrt`
81×	`*-un-lft-identity`
71×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
44×	`sqr-pow`
18×	`difference-of-squares`
15×	`sqrt-prod` `log-pow`
14×	`exp-prod`
9×	`pow1`
8×	`add-log-exp`
7×	`fma-neg`
5×	`add-exp-log`
4×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-unpow` `fma-def`
2×	`sub-neg` `sqrt-pow1`
1×	`+-commutative` `pow-to-exp` `log-div` `flip3--` `flip3-+` `pow1/2` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `pow-exp` `sum-log` `sqrt-pow2` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 216

Calls

4 calls:

9.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
17.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)
128.0ms	(log (exp (- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))))
25.0ms	(- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))

series2.4s

Counts

4 → 12

Calls

4 calls:

516.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
772.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)
562.0ms	(log (exp (- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))))
589.0ms	(- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))

simplify2.4s

Counts

228 → 228

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	473	13007
1	926	9144
2	2467	6670
done	5000	4625

prune837.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes288.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.7b

bsearch276.0ms

Steps

Iters	Range		Point
9	5.155942382976535e-09	0.21963308938311268	0.0028097389045321224
11	-2445851338.3862987	-4.2674702477225e-16	-0.002686087558037088

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	49	144
1	51	144
done	51	144

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.2s	2838×	body	1280	valid
278.0ms	4087×	body	80	valid
155.0ms	607×	body	640	valid
152.0ms	327×	body	320	valid
16.0ms	141×	body	160	valid